Sum it Up, Angle Edition: Part 2

There is a little bit of mystery and magic to these relationships, if you don’t believe me just ask Mr. Vaudrey.  Students trust that a triangle is simple, yet if you asked them to communicate anything beyond the magical balance of 3 angles, and 3 sides, most wouldn’t know what else is true.  Sometimes students see triangles as  snowflakes, each one of them unique.  Little do they know how much all these triangles are alike.

The Hook:

1. Get quarter sheets of graph paper
2. Draw your own unique triangle
3. Color in the angles in each corner
4. Cut Out the triangle
5. Tear off each corner
6. Piece together the puzzle, and what do you see?

Playtime:

http://www.geogebratube.org/student/m96801

Practice:

Describe in your own words what’s happening.

This is HUGE.  Students need time to digest this transformation.  If it feels like the engine is stalling, change gears:

Start practicing lo-tech with some paper examples.

Recursive Reflection

Constantly bring back the triangle with the transforming corners.  Have the students take some

Then go back again to the applet.  Get the class to a point where students are articulating what is happening in the triangle.  Have them say it in multiple ways.  These angle relationships have patterns and consistencies, but often get lost in the multiple perspectives (what about this corner, or that one, or the inside, or the out, or what does a parallel line have anything to do with it).  If students can transform a triangle and its angles, then adding in the relationships with parallel lines is only a half step away.

Don’t forget to check out the other gems over at Transformulas.

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